Full NLO initial-state-radiation calculation for inclusive J/psi plus eta_c production

Calculate the initial-state-radiation corrections at full next-to-leading-order accuracy for each color-singlet-plus-color-singlet, color-singlet-plus-color-octet, and color-octet-plus-color-octet channel in inclusive e+e− → J/ψ + ηc + X production.

Background

The analysis does not include initial-state radiation (ISR), even though ISR can modify inclusive charmonium cross sections. The authors estimate that ISR may moderately enhance the total NRQCD prediction without changing the qualitative importance of color-octet contributions, but they do not calculate the corrections explicitly for the individual production channels. A complete channel-by-channel NLO ISR calculation is therefore left unresolved and is needed for a more definitive comparison with experiment.

References

This estimate, however, awaits a more definitive assessment based on a full NLO calculation of the ISR corrections to the individual channels.

— Inclusive productions of $J/ψ+η_c$ in $e^{+}e^{-}$ annihilation at Belle  (2609.09590 - Sun et al., 9 Sep 2026) in Section 3, Phenomenological Results, final paragraph before Section 4